What Is the Role of the Risk-Free Rate in the Black-Scholes-Merton Model?

The risk-free rate is a crucial input in the Black-Scholes-Merton (BSM) model, representing the theoretical return on a riskless investment over the option's life. It is used to discount the expected future payoff of the option back to its present value.

It also influences the forward price of the underlying asset, which is a component of the option's pricing.